Vertical Forces & Acceleration Practice Problems

A cable with negligible mass is connected to a crate with a mass of 5.00 kg that is resting on a smooth, flat surface. The cable then passes over a light, smooth pulley. Another crate, with mass m, is attached to the other end of the cable. The crates are released, leading to a tension of 20.0 N on the cable. Compare the tension (T) to the weight (w) of the hanging crate.

Shown below are three boats being pulled along the x-axis on a frictionless surface via ropes. If the magnitude of the pull force applied is 480 N, calculate the tension in each rope.

Two crates, each weighing 100.0 N, are dangled at opposite ends of a cable that passes over a smooth pulley. The pulley is attached to the roof by a rope. Calculate the tension in the rope. Assume that the pulley and cable have negligible mass.

Two blocks, each weighing 50.0 N, are dangled at either end of a cable. The cable passes through a smooth pulley, which is attached to the roof by a rope. Calculate the tension in the cable. Assume that the mass of the pulley and the cable are negligible.

On the Earth's surface, a cucumber weighs 2.94 N. If the acceleration due to gravity on the Moon's surface is 1.63 m/s², calculate the mass of the cucumber and its weight on the surface of the moon.

An apple weighs 1.0 N at the surface of the earth. What is the apple's mass on the earth's surface?

The ratio of the weight of a person on the surface of Mars to that on the surface of Earth is 0.38. Find the acceleration due to gravity on the surface of Mars.

A boy weighs a bag of tomatoes using a spring scale attached to the ceiling of a lift. While the elevator is at rest, he measures a weight of 40.0 N. As the lift starts moving upward, what is the acceleration of the lift if the scale reads 48.1 N?

A massless rope is connected to a slab that has a mass of 5.00 kg that rests on a horizontal, frictionless table. The rope passes over a light, smooth pulley at the edge of the table and is attached to a hanging slab with a mass of m. The rope has a tension of 20.0 N. What is the acceleration of the system when the two slabs are released?

Three boats each of mass 20.0 kg are being pulled horizontally on a frictionless surface using ropes as shown in the image. What is the acceleration of the boats, if the force applied is of magnitude 480 N?

A girl with a normal weight of 980 N is standing on a weighing scale situated in a lift that is moving upwards. At the same time, she is holding a 4.00 kg packet by a light vertical string. What is the tension on this string when the lift has an upward acceleration of 3.0 m/s²?

A person draws a bucket of water from a well, where the bucket is accelerating at 4.00 m/s² upwards. The rope attached to the bucket pass over a light pulley and has a tension of 20.0 N. Calculate the mass of the bucket of water.

A heavy steel ball with a mass of 150 kg is suspended from a massive, strong, uniform rope with a mass of 25.0 kg. Calculate the tension in the rope

(i) at a point one-fifth of the way up from the bottom

(ii) at a point two-thirds of the way up from the bottom.

A 15.0-kg bucket full of water is being pulled up from a well 20 m deep by a long uniform rope having a mass of 10 kg. If the bucket starts at rest, calculate the time it takes for it to be lifted out of the well at maximum acceleration. Assume that the rope has uniform strength and at any point, can support a maximum tension not exceeding 5.0 times its weight without breaking.

A boy with a normal weight of 980 N is standing on a weighing scale kept in a lift that is moving upwards. If the lift has an upward acceleration of 3.0 m/s², what is the reading on the scale?

Ali's office is on the ground floor of a research center.  He takes an elevator to get to the third floor. His velocity versus time graph in the elevator is shown in the figure. If his mass is 60kg calculate his weight at i) t = 2 s, ii) t = 5 s, and iii) t = 7 s.

Two patients X (60kg) and Y(85kg) are in an elevator descending at a rate of 15m/s. Patient X exits the elevator on the sixth floor. Suppose it takes the elevator 8s to stop on the 6th floor, calculate the weight of both patients before the elevator begins to slow down.

A private company provides high-quality elevators for both public and private buildings. If their newly designed elevator reaches 15 m/s in eight seconds, determine the weight of an 85 kg load before the elevator began moving.

An engineer tests an elevator. During the test, it takes the elevator 6s to reach 14 m/s. He then places a 65kg object in it.  Find out how much the object weighs when the elevator is moving at 14 m/s.

Mass is a property of matter; weight is a force. What is the approximate weight of a man on earth if he has a mass of 85 kg?

If the distance between Earth and a geostationary satellite weighing 1600 kg is approximately 35,800 kilometers, determine the satellite's acceleration towards Earth using equations of motion. The mass of the earth is 5.9× 10²⁴ kg.

Jimmy and his friend make a contraption with a horizontal mass-spring system. In the first trial, they attach a 68 kg mass to the spring and set it to oscillate. Assume the oscillating object's position is given by x = (0.240 m) cos ((π rad/s) × t). At time t = 2 s, how much force does the spring exert on the object?

A string is used to suspend a bucket. Find the tension in the string if the bucket rises at a constant speed of 8 metres per second. The mass of the bucket is 25 kg.

Determine the tension in the string when the string holds up a 60 kg box. The box's v_y is 8.0 m/s, and its acceleration is 8.0 m/s².

A missile, with a mass of 2.65 x 10⁶ kg, is launched vertically by applying a force of 3.45 x 10⁷ N through gas expulsion. Ignoring the mass of the expelled gases and assuming constant gravitational acceleration, what is the missile's acceleration?

A man stands on a weighing scale inside a stationary lift. When the lift moves, the scale temporarily displays 0.85 of his actual weight. Determine the lift's acceleration and indicate whether it moves upwards or downwards.

What weight appears on a weighing scale for the mass of a 55.0-kg man in a lift that ascends steadily at 3.4 m/s?

What weight appears on a spring scale for the mass of a 56.0-kg person in a lift that descends steadily at 5.4 m/s?

What is the weight reading on a weighing scale for a 59.0-kg passenger inside a lift that descends with a constant acceleration of 0.17g?

What weight appears on a weighing scale for a 52.0 kg passenger in a free-fall lift?

A 5.00-kg cat holds a lift's rope and snaps at force 100 N. Calculate the lift's minimum acceleration (magnitude and direction).

In a physics experiment, a wooden block of mass $M_1$ is placed on a frictionless table and connected through a pulley to a hanging nylon block of mass $M_2$. The system is linked by a nylon cord with a mass $M_{C}$ , which passes over a frictionless pulley, as shown. The cord is divided into two segments with lengths $L_1$ on the table side and $L_2$ on the hanging side, where the total length of the cord is $L=L_1+L_2$. Derive an equation to determine the acceleration $a$ of the system.

A service elevator in a large hotel is designed to transport equipment vertically with minimal discomfort to the operator while ensuring efficiency. The elevator's movement from the ground floor to a maintenance level 120 meters above involves three distinct phases:

(1) It accelerates from rest with a constant acceleration of 1.0 m/s² until it reaches its cruising speed of 5.0 m/s.

(2) It then travels at this constant speed for the majority of its vertical journey.

(3) Finally, it decelerates at a constant rate of 1.0 m/s² until it comes to rest at the maintenance level.

Determine the elapsed time for each of these 3 stages of the elevator's ascent.

A scientist is experimenting in a hot air balloon going upwards at a constant speed. The basket of the balloon has an inclined plane fixed with the floor making an angle of 43° with it. If a block of mass M slides without friction on the incline, evaluate the acceleration of the block relative to the inclined plane.

A compact but dense yarn reel has a radius of R and a mass of M. To keep the reel's center of mass stationary in mid-air while you draw the yarn upwards and it unravels, determine the force required to apply to the yarn.

Calculate the tension a cable must sustain if it lifts an 1100-kg elevator upwards with an acceleration of 0.75 m/s².

Suppose an object is thrown vertically downward from a certain height with an initial velocity of 2.0 m/s at t=0. Considering the presence of a resistive force F=-kv opposing its motion, in addition to gravity, determine the object's velocity as it falls.

In a classroom demonstration, five different masses (1.0 kg, 1.2 kg, 1.4 kg, 1.6 kg, and 1.8 kg) are suspended from a horizontal bar using strings as shown in the figure below. Each string has a maximum tension of 25 N before breaking. When this setup is placed in a lift accelerating upward, only the strings attached to the 1.0-kg, 1.2-kg, and 1.4-kg masses remain intact. Determine the range of acceleration for the elevator.

A helicopter is flying still in the air. An inclined plane is fixed to the floor of the helicopter inside it, making an angle of 35° with the floor. A book of mass M slides without friction on the inclined plane. If the helicopter starts to fall freely, what would the acceleration of the book be relative to the plane?

A 2.5 kg cat jumps 0.50 m off the ground. Before jumping, it squatted a distance of 0.060 m. Assuming the force exerted on the cat by the ground acts over this distance find the force exerted by the cat against the ground to jump.

A 6850-kg cargo plane ascends at 0.75 m/s² while lifting a 1100-kg container. If the rope's mass is negligible, measure the tension in the rope connecting the container to the plane.

A 6800-kg aircraft ascends at 0.82 m/s² while lifting an 1150-kg container. Determine the magnitude of the force exerted on the aircraft by the rope.

A 180g damp sponge, starting from rest, slips smoothly down a 3.5m slope at 9.5°. Determine the time it takes for the sponge to reach the bottom. Does altering the sponge's mass to 280g affect this duration?

An angler pulls a trout directly upwards from the water at an acceleration of 3.5 m/s² with a thin rope capable of withstanding up to 22.5 N (about 5lb). If the rope breaks, the trout escapes. What does the rope breaking indicate about the trout's mass?

A construction crane lifts a steel girder with a mass of 800 kg at an acceleration of 0.20g to a certain height on a building site. Calculate the tension in the lifting cable while the girder is accelerating.