Newton's First & Second Laws Practice Problems

A truck of mass 8900 kg is accelerated at 0.5g. If the same force is used to accelerate an SUV of mass 2300kg, calculate the SUV's acceleration. Express the acceleration as multiples of g.

When a vehicle takes off abruptly, you will jerk backward. To gain a better comprehension of the process,  you place a box on a frictionless surface at the back of a pick-up truck. There is no mechanism to secure the box. Explain what happens when the pick-up truck takes off.

A 140 kg drone runs out of fuel at a high altitude near the earth's poles. The drone has no safety gear such as a parachute. It begins falling towards the earth's surface and crushes into the snow at 278 km/h penetrating a depth of 68.0 cm. Determine the force exerted on the drone by the snow during the crush expressed in Newtons. What multiple of its weight is this?

A 125 kg drone in flight runs out of fuel at a high altitude near the earth's poles. The drone has no safety gear such as parachutes. It begins falling towards the earth's surface and crashes into the ice at 285 km/h penetrating a depth of 59.0 cm. Determine its acceleration during the crash in m/s² and multiple's of g, assuming constant acceleration.

As part of a physical exercise, a gymnast jumps straight up from a crouched position attaining a maximum height of approximately 60 cm. However, the gymnast's body above the knees rises approximately 52 cm above the ground. To simplify the calculations while yielding a realistic result, we shall make an assumption that the whole body rises 60 cm during the jump. What free-body diagram best represents the gymnast while he is pushing up from the ground?

A 2.90 kg box rests on a horizontal, frictionless surface. A light string is attached to the box that runs through a massless and frictionless pulley to suspend a box of mass m with its other end. The boxes are released and the tension in the string is found to be 9.80 N. Draw one free-body diagram for each box.

An engineer has designed a 1.28 × 10⁴ kg space vehicle. The vehicle is to be launched vertically upward. A co-engineer decides to accelerate the space vehicle as fast as possible to a speed of 290 m/s. However, an astronaut in the space vehicle will black out if the acceleration exceeds 4g. Determine the force exerted on the astronaut by the space vehicle in terms of the astronaut's weight, w. The astronaut's free-body diagram will be helpful.

An engineer has designed a 6.32 × 10⁵ kg space vehicle. The vehicle is to be launched vertically upward. A co-engineer decides to accelerate the space vehicle as fast as possible to a speed of 350 m/s. However, an astronaut in the space vehicle will black out if the acceleration exceeds 4g. Determine the maximum thrust generated by the spacecraft's engines at the brink of blackout. The spacecraft's free-body diagram will be helpful.

An engineer has designed a demo spacecraft of mass 12.0 kg. The spacecraft's engine burns fuel exerting a time-varying force on the spacecraft as it cruises vertically upward. The forces obeys the relation F(t) = A + Bt². The force is measured at various instants of time. It is found that the force at t = 0 s is 60 N and the force after 2.60 s is 112 N. Determine the value of A and B including their SI units. You may assume that the spacecraft's mass is constant. 

An 8.50 kg trolley is accelerating in a straight line in the x-axis direction. The acceleration of the trolley as a function of time is shown in the graph below. Determine the times when the trolley experiences a constant net force. 

A 3.60 kg trolley is accelerating in a straight line in the x-axis direction. The acceleration of the trolley as a function of time is shown in the graph below. Determine the maximum net force on the trolley and the time when the maximum force is experienced. 

A 0.875 kg toy truck is initially at rest on a horizontal frictionless surface. The initial position is the origin (x = 0). A child applies a force in the positive direction parallel to the x-axis and equal to 1.50 N at t = 0 on the toy. The force is withdrawn at t = 1.80 s. The force is once again applied at t = 4.20 s and continues to be applied until t = 7 s. Determine the speed and position of the toy at t = 6.50 s.

A 25.0 kg unloaded sleigh is initially at rest on a horizontal frictionless ice surface. The initial position is the origin (x = 0). A worker applies a force parallel to the x-axis of 80.0 N at t = 0 on the sleigh. The force is withdrawn at t = 2.50 s. Determine the speed and position of the sleigh at t = 2.50 s.

A worker pushes a sled using a constant horizontal force of magnitude 80N over a smooth ice surface. Starting from rest, the sled covers 8.70 m in 2.60 s. Determine the mass of the sled. Assume friction force is negligible.

A block of wood lies on ice. The ice surface can be approximated to be a horizontal, frictionless surface. A  man decides to move the block and applies a horizontal force of magnitude 140 N on the block. The block accelerates at 4.26 m/s². Determine the mass of the block.

Straps are used to manage forces on body parts with injury. In one instance, a patient with a jaw injury requires a net upward force of 8.0 N applied on the chin using a strap. If the strap has uniform tension throughout its length and the angle between T₁ and T₂ is 65°, what tension should be set in the strap to provide the desired upward force?

To unearth an old relic buried in the ground, three workmen apply three horizontal vector forces on the relic using ropes as shown below. Determine the magnitude and direction of the resultant force from the three pulls using components. 

Three archeologists pull on an old relic buried in the ground using three horizontal ropes. The image below shows the applied force vectors. Determine the x-and y-components for the three pulls. 

A gardener uses two bulls to uproot a stump in the garden. The bulls pull horizontally on ropes tied to the stump. If the angle between the two ropes is 40.0, Black and White pull with forces of 750 N and 860 N respectively, what is the magnitude and direction of the resultant force measured from White's rope? 

The force-acceleration curves of three blocks pulled by ropes with equal strength are shown below. If block 2 has a mass of 4.5 kg, Determine the masses of blocks 1 and 3.

A net force with only a y-component, F_y, is applied on a 1500g metal block moving parallel to the y-axis. You are provided with an acceleration-time graph of the block. Sketch a force-time graph for the block.

Ramps are useful machines when loading trucks. In one instance, a worker pulls on a trolley being loaded on a truck with an upward force F that has a direction of 26.0° with the ramp. If the ramp has a slope angle of 18.0°, what force magnitude F must the worker apply to generate an F_x component parallel to the ramp equal to 68.0 N? 

Ramps are useful machines when loading trucks. In one instance, a worker pulls on a trolley being loaded on a truck with an upward force F that has a direction of 28.0° with the ramp. If the ramp has a slope angle of 15.0°, what is the value of the component F_y perpendicular to the ramp when the F_x component parallel to the ramp is equal to 86.0 N? 

The tires of a pickup truck push against the road with a uniform force, accelerating the truck at 6.5 m/s². Determine the new acceleration when the force between the road and tires is reduced to 3/4 of the original value.

A uniform net force accelerates a car at 8.2 m/s². Calculate the resulting acceleration if the uniform net force is reduced to 3/5 of the initial value and is now applied to a truck with 1.5 times the car's mass.

A net force directed purely in the y-direction is applied on a 10 kg cart that coasts parallel to the axis. The force-time graph is provided. Work out the acceleration time graph of the cart.

A computerized scientific probe is used to measure the net force acting on an object and the resulting acceleration. The probe creates the acceleration-force graph shown. Determine the object's mass.  

Two buckets of sand hang on a frictionless pulley. They are connected with a massless cable such that if one bucket moves up, the other moves downward. The bucket moving downward has an acceleration of 0.6g (where g is the acceleration due to gravity) and a mass of 14.0 kg. Determine the mass of the bucket moving upward.

Two blocks are connected with a cable through a pulley. The heavier block (70.0 kg) takes 5.5 s to cover 1.5 m from rest. Determine the mass of the lighter block. Assume the pulley is frictionless and massless.

The diagram shown is the free-body diagram of a block. Determine the direction of the acceleration vector and label it on the image. You may use a = 0 if the block is not accelerating.

A 13-kg model airplane hangs from a tree branch on a thin vertical rope. If the length of the rope is 1.5 m, what horizontal force is required to move the hanging airplane 0.50 m to any one side from its equilibrium position?

A 13-kg piñata is suspended vertically from a tree branch using a rope. If the length of the rope is 1.5 m, and the piñata is displaced 0.50 m to one side from its equilibrium position, what would be the tension in the rope?

A sparrow's heart, at each heartbeat accelerates about 30 g of blood from 0.45 m/s to 0.65 m/s within 0.20 s. What is the force applied by the sparrow's heart muscle?

A crate is dropped from a platform 1.9 m above the ground. Upon impact, it comes to a stop over a distance of about 0.6 m as it compresses a cushioning material. If the mass of the crate is 30 kg, calculate the average force exerted by the cushioning material to decelerate the crate over this distance.

A race car weighing 1000 kg accelerates from a standstill to its top speed of 200 km/h along a straight roadway. During acceleration, the car applies a maximum horizontal force of 6000 N against the road. Upon reaching its maximum velocity, the magnitude of the exerted force by the car is 2000 N. Calculate (i) the maximum acceleration of the race car, (ii) the combined force of friction and air resistance when the car is at its top speed.

A 15-kg suitcase is tied to the rear end of a motorbike as shown in the figure below. While driving at 30 km/h, the motorbike suddenly stops in 0.2 s due to a traffic signal. Assuming uniform deceleration during this movement, calculate the net horizontal force exerted by the rope on the suitcase to prevent it from falling forward.

The wind causes a speck of dust, 2.0 µm in diameter, to float in the air. If the force exerted on it is 20pN (piconewtons) and its density is 0.5 g per cm³. Calculate its acceleration in g's.

A crate weighing 50 kg is placed onto the flatbed of a carrier truck that's traveling horizontally at a constant speed of 15 m/s as shown in the figure below. The coefficient of kinetic friction (μ_k) between the crate and the flatbed is 0.2. Determine the duration required for the crate to cease all motion after it's positioned on the moving flatbed.

A weightlifter tries to stop a 2.5 x 10² kg rolling barbell moving at 43 km/h to keep it from hitting a fragile structure 5.0 x10¹ m away. What force must he exert on the barbell? Give it as a percentage of the weight of the barbell. What force would the barbell exert on the weightlifter as a result?

A small ball hangs from the ceiling of a bus by a cord. As the bus gradually speeds up from a standstill to 24 m/s in 4.0 s, what angle Φ is formed by the cord with the vertical?

Find the velocity of a 2.0-kg block at t = 3.0s, initially at rest, when subjected to two forces: $\overrightarrow{F_1}$ = (17$\overrightarrow{i}$ + 13$\overrightarrow{j}$)N, $\overrightarrow{F_2}$ = (-11$\overrightarrow{i}$ + 23$\overrightarrow{j}$)N.