If a 35 g arrow moving at 160 km/h penetrates a block of wood suspended by a rope, what impulse is delivered to the block? (Answer: 1.56kg * m/s)
What velocity will the wood block acquire if its mass is 7.0 kg? Ignore the mass of the arrow compared to that of the wood block. (Answer: 0.222m/s)
Please show all work on how to get those answers.
To the first problem, you need to convert all the numbers to the correct units.
35 kg = 0.035 kg
160 km/h = 44.44 m/s (Hint: to convert km/h quickly to m/s, divide by 3.6)
So, it is asking for the impulse which is
Imp = mv
Imp = (0.035 kg)(44.44 m/s) = 1.56 kg-m/s
To the second problem, you are trying to find the velocity assuming the impulse is the same.
v = p/m
v = (1.56 kg-m/s) / (7.0 kg) = 0.222 m/s
To find the impulse delivered to the block, you can use the formula:
Impulse = change in momentum
The momentum of an object is the product of its mass and velocity.
Given:
Mass of the arrow (m1) = 35 g = 0.035 kg
Velocity of the arrow (v1) = 160 km/h
First, we need to convert the velocity from km/h to m/s. The conversion factor is 1 km/h = 0.27778 m/s.
So, v1 = 160 km/h * 0.27778 m/s = 44.4444 m/s
The momentum of the arrow (p1) can be calculated as:
p1 = m1 * v1 = 0.035 kg * 44.4444 m/s = 1.55555 kg·m/s ≈ 1.56 kg·m/s
Therefore, the impulse delivered to the block is approximately 1.56 kg·m/s.
To find the velocity acquired by the wood block, we can use the principle of conservation of momentum:
Initial momentum = Final momentum
The initial momentum is the momentum of the arrow, which we found to be 1.56 kg·m/s.
Given:
Mass of the wood block (m2) = 7.0 kg
Initial velocity of the wood block (v2_initial) = 0 (since it is at rest initially)
Final momentum = m2 * v2_final
Since the mass of the arrow is negligible compared to the wood block, we can assume that the total momentum after the arrow hits the wood block is conserved.
Therefore, we can write:
1.56 kg·m/s = 7.0 kg * v2_final
And solving for v2_final:
v2_final = (1.56 kg·m/s) / 7.0 kg
v2_final ≈ 0.222 m/s
Therefore, the velocity acquired by the wood block, disregarding the mass of the arrow compared to the wood block, is approximately 0.222 m/s.