A block of mass M is released from rest near the top of a ramp that is inclined at an angle θ with the...

Question

A block of mass M is released from rest near the top of a ramp that is inclined at an angle θ with the horizontal as shown in the figure. The block slides down the ramp with negligible friction, traveling a distance d in a time t. The angle of the ramp is then decreased.

Which of the following describes the changes, if any, in the net force exerted on the block, the acceleration of the block, and the distance the block travels in time t ?

SnapAndSolve AI · Accepted Answer

Changes in the Net Force, Acceleration, and Distance

1. Net Force on the Block

The net force acting on the block is given by the component of the gravitational force acting parallel to the ramp. This force can be expressed as:

F_net = M * g * sin(θ)

Where M is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the ramp. When the angle θ is decreased, sin(θ) also decreases. Consequently, the net force exerted on the block will decrease as the angle of the ramp decreases.

2. Acceleration of the Block

The acceleration of the block can be calculated using Newton's second law:

a = F_net / M = g * sin(θ)

Since we have established that the net force decreases with a decrease in θ, the acceleration of the block will also decrease as the angle of the ramp decreases.

3. Distance Traveled by the Block in Time t

The distance traveled by the block can be found using the kinematic equation:

d = (1/2) * a * t²

With the block's acceleration decreasing as the angle θ is decreased, the distance d will also decrease for the same time interval t.

Summary of Changes

Net Force: Decreases
Acceleration: Decreases
Distance: Decreases

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A block of mass M is released from rest near the top of a ramp that is inclined at an angle θ with the...

Answer

Changes in the Net Force, Acceleration, and Distance

1. Net Force on the Block

2. Acceleration of the Block

3. Distance Traveled by the Block in Time t

Summary of Changes

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