Multi-Body Systems Archives • Nerd Notes

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What we found:

Four blocks of masses \( 20 \, \text{kg}, \, 30 \, \text{kg}, \, 40 \, \text{kg}, \, \text{and} \, 50 \, \text{kg} \) are stacked on top of one another in an elevator in order of decreasing mass with the lightest mass on the top of the stack. The elevator moves downward with an acceleration of \( 3.2 \, \text{m/s}^2 \). Find the contact force between the \( 30 \, \text{kg} \) and \( 40 \, \text{kg} \) masses.

Two masses, \(m1\) and \(m2\), are connected by a cord and arranged as shown in the diagram with m1 sliding along on a frictionless surface and \(m2\) hanging from a light frictionless pulley. What would be the mass of the falling mass,\(m2\), if both the sliding mass,\(m1\), and the tension, \(T\), in the cord were known?

The figure shows a truck pulling three crates across a rough road. Which of the following shows the directions of all the horizontal forces acting on crate 2?

Three blocks are stacked on top of one another. The top block has a mass of \( 4.6 \, \text{kg} \), the middle one has a mass of \( 1.2 \, \text{kg} \), and the bottom one has a mass of \( 3.7 \, \text{kg} \). Identify and calculate any normal forces between the objects.

A block hangs from the ceiling by a massless rope. A \( 3.0 \, \text{kg} \) block is attached to the first block and hangs below it on another piece of massless rope. The tension in the top rope is \( 63.0 \, \text{N} \).

When a horizontal force of \( 4.5 \, \text{N} \) acts on a block on a resistance-free surface, it produces an acceleration of \( 2.5 \, \text{m/s}^2 \). Suppose a second \( 4.0 \, \text{kg} \) block is dropped onto the first. What is the magnitude of the acceleration of the combination if the same force continues to act? Assume that the second block does not slide on the first block.

A simple Atwood’s machine remains motionless when equal masses \(M\) are placed on each end of the chord. When a small mass \(m\) is added to one side, the masses have an acceleration a. What is \(M\)? You may neglect friction and the mass of the cord and pulley.

Three blocks of masses 1.0, 2.0, and 4.0 kilograms are connected by massless strings, one of which passes over a frictionless pulley of negligible mass, as shown above. Calculate each of the following.

Three blocks of masses m3 = 1.0, m2 = 2.0, and m1 = 4.0 kilograms are connected by massless strings, one of which passes over a frictionless pulley of negligible mass, as shown above.

A pulley system consists of two blocks of mass \( 5 \) \( \text{kg} \) and \( 10 \) \( \text{kg} \), connected by a rope of negligible mass that passes over a pulley of radius \( 0.1 \) \( \text{m} \) and mass \( 2 \) \( \text{kg} \). The pulley is free to rotate about its axis. The system is released from rest, and the block of mass \( 10 \) \( \text{kg} \) starts to move downwards. Assuming that the coefficient of kinetic friction between the pulley and the rope is \( 0.2 \), and neglecting air resistance, determine

Three blocks of masses 5, 4, and 3 kg are placed side by side in that order. A 25 N force applied on the 5 kg block accelerates all three blocks together to the right. Find the acceleration of the blocks and the normal force the 4 kg block exerts on the 3 kg block.

A 1 kg and unknown mass M hangs on opposite sides of the pulley suspended from the ceiling. When the masses are released, M accelerates down at 5 m/s2. Find the value of M.

Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle \( \theta \) to the horizontal. If the coefficients of friction are \( \mu_A = 0.2 \) and \( \mu_B = 0.3 \) and if \( m_A = m_B = 5.0 \) \( \text{kg} \), determine:

Block m1 is stacked on top of block m2. Block m2 is connected by a light cord to block m3, which is pulled along a frictionless surface with a force F as shown in the diagram. Block m1 is accelerated at the same rate as block m2 because of the frictional forces between the two blocks. If all three blocks have the same mass m, what is the minimum coefficient of static friction between block m1 and block m2?

In the diagram shown a 20 N force is applied to a 7 kg mass. Assume frictionless conditions. Calculate the acceleration of the system Calculate the normal force between the 2 masses Bonus: What would happen to the acceleration and normal force if the force was applied to block A instead

In the diagram below, A has a mass of 3.2 kg and B a mass of 2.4 kg. The pulley is frictionless and has no mass. Calculate the acceleration of the system Calculate the tension in the string If mass A is released from a height of 0.5 m above the ground, what will be its speed just before it hits the floor.

Two objects (49.0 and 24.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find the acceleration of the objects and the tension in the string.

A train consists of 50 cars, each of which has a mass of 6.1 x 103 kg. The train has an acceleration of 8.0 × 10-2 m/s2?. Ignore friction and determine the tension in the coupling at the following places: between the 30th and 31st cars between the 49th and 50th cars