A horizontal force of 0.80N is required to pull a 5kg bullet across a table top at a constant speed. With the block initially at rest, a 20g bullet fired horizontally into the block causes the block to slide 1.5m before coming to rest again. Determine the speed V of the bullet where the bullet is assumed to be in the block
Answer the question
To determine the speed V of the bullet when it is assumed to be in the block, we can use the principles of conservation of momentum and conservation of energy.
Step 1: Calculate the initial momentum of the block before the bullet is fired.
The initial momentum of the block is given by the product of its mass (m_block) and the initial velocity (v_block) which is zero since the block is initially at rest:
Initial momentum of the block = m_block * v_block = 5 kg * 0 m/s = 0 kg·m/s
Step 2: Calculate the momentum of the block after the bullet is fired.
The momentum of the block after the bullet is fired can be calculated by considering the momentum conservation.
The momentum before the bullet is fired is equal to the momentum after the bullet is fired.
Initial momentum of the block = Final momentum of the block
Step 3: Calculate the momentum of the bullet.
The momentum of the bullet can be calculated by considering the momentum conservation.
Since the bullet is assumed to be inside the block, the total system momentum after the bullet is fired can be calculated as the sum of the momenta of the block and the bullet.
Final momentum of the block + momentum of the bullet = m_block * v_block_final + m_bullet * v_bullet
Step 4: Solve for the final velocity of the block and bullet system.
Since the block comes to rest after sliding a certain distance, the final velocity of the block (v_block_final) is zero.
0 kg·m/s + momentum of the bullet = 5 kg * 0 m/s + 0.02 kg * v_bullet
momentum of the bullet = 0.02 kg * v_bullet
Step 5: Use the definition of momentum to calculate the momentum of the bullet.
The momentum of the bullet is given by the product of its mass (m_bullet) and its velocity (v_bullet):
momentum of the bullet = m_bullet * v_bullet
Step 6: Equate the momentum of the bullet from Step 5 with the momentum of the bullet from Step 4.
0.02 kg * v_bullet = 0.02 kg * v_bullet
Step 7: Solve for the speed V of the bullet.
Since the bullet is assumed to be inside the block, its speed is the same as the speed of the block when they both come to rest.
Therefore, v_bullet = V
Hence, the speed of the bullet is V.
So, the speed of the bullet, V, is equal to the speed of the block when they both come to rest.
To determine the speed of the bullet when it is assumed to be in the block, we can start by analyzing the situation.
Given:
- Horizontal force required to pull the bullet across the table top = 0.80 N
- Mass of the block = 5 kg
- Distance the block slides before coming to rest again = 1.5 m
- Mass of the bullet fired into the block = 20 g (0.02 kg)
To solve this problem, we can apply the principle of conservation of momentum.
The momentum of an object is given by the formula:
Momentum = Mass × Velocity
Before the bullet is fired into the block, the block is moving with a constant speed. This implies that the momentum before and after the bullet is fired should remain the same.
The initial momentum of the block is:
Initial momentum of the block = Mass of the block × Initial velocity of the block
Since the block is initially at rest, the initial velocity of the block is 0. Therefore, the initial momentum of the block is also 0.
After the bullet is fired into the block, the block and the bullet move together with a common final velocity V.
The final momentum of the block and the bullet combined is:
Final momentum = (Mass of the block + Mass of the bullet) × Final velocity (V)
Now, we can set up an equation based on the principle of conservation of momentum:
0 = (Mass of the block + Mass of the bullet) × V
Substituting the given values:
0 = (5 kg + 0.02 kg) × V
Simplifying the equation:
0 = 5.02 kg × V
Since the mass of the bullet is very small compared to the mass of the block, we can neglect it in the equation. This assumption is valid when the bullet is embedded within the block and their masses are considered together.
0 = 5 kg × V
0 = 0 kg⋅m/s (Since the initial velocity of the block is 0)
Therefore, the speed (V) of the bullet when it is assumed to be in the block is 0 m/s.
mu m g = .8 N
mu*5*9.81 = .8 N
mu = .8 /(5*9.81)
work done by friction during stop =mu 20 *9.81 * 1.5 meters
so
(1/2) (20) v^2 = [ .8 /(5*9.81) ] 20* 9.81 * 1.5
10 v^2 = [ .8 ] 4 * 1.5