# 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 k/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/s^{2} and multiple's of g, assuming constant acceleration.

As part of a physical exercise, a gymnast jumps straight up from a crouched position during a physical exercise 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 person while jumping?

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 × 10^{4} 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 × 10^{5} 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 + Bt^{2}. 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 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. 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/s^{2}. 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 T_{1} and T_{2} 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?