1) A box with a mass of 17 kg is moving at a velocity of 3.75 m/s. If the box was pushed with a force of 75 N how far did it go?
2) Calculate the momentum for a 0.18 kg rifle bullet traveling 369 m/s.
3) What is the impulse needed to stop the bullet?
4)Ice has a specific heat of 2060 J/kg K. How much heat must be absorbed by 2.0 kg ice at-20.0 degree Celsius to raise it up to 0.0 degree celsius, before any melting actually takes place?
1)
F=ma =>
a=F/m = 75/17 = 4.4 m/s²
s=v²/2a=3.75²/2•4.4=1.6 m
2)
p= mv=0.18•3.75 =...
3) Impulse =mv=0.18•3.75 =...
4) Q=mcΔT=2•2060•20 = ...
1) To find the distance the box traveled, we can use the formula:
distance = (force * time) / mass
Given:
mass = 17 kg
velocity = 3.75 m/s
force = 75 N
First, we need to find the time taken by the box to come to rest. Since the box is moving with a constant velocity, we can use the formula:
velocity = acceleration * time
Rearranging the formula:
time = velocity / acceleration
Since the box is coming to rest, the acceleration will be the opposite of the initial velocity:
acceleration = -velocity
Plugging in the values:
time = 3.75 m/s / (-3.75 m/s) = -1 second
Negative sign indicates the change in direction.
Now, we can use the formula to calculate the distance:
distance = (force * time) / mass
distance = (75 N * -1 s) / 17 kg
distance = -4.41 m
The box traveled 4.41 meters before coming to rest.
2) Momentum is calculated using the formula:
momentum = mass * velocity
Given:
mass = 0.18 kg
velocity = 369 m/s
Plugging in the values:
momentum = 0.18 kg * 369 m/s
momentum = 66.42 kg*m/s
The momentum for the bullet is 66.42 kg*m/s.
3) Impulse is the change in momentum and is calculated using the formula:
impulse = force * time
Given:
force = unknown
time = unknown
momentum = 66.42 kg*m/s (from previous calculation)
We need to find the force, so rearranging the formula:
force = impulse / time
Since the bullet comes to a stop, its change in momentum is equal to the initial momentum:
impulse = change in momentum = final momentum - initial momentum
impulse = 0 - 66.42 kg*m/s
impulse = -66.42 kg*m/s
Assuming the stopping time is negligible, we can use the equation:
force = impulse / time
force = (-66.42 kg*m/s) / (negative time) = 66.42 N
The impulse needed to stop the bullet is 66.42 N.
4) To calculate the heat required to raise the temperature of ice, we can use the formula:
heat = mass * specific heat * change in temperature
Given:
mass = 2.0 kg
specific heat = 2060 J/kg K
initial temperature = -20.0 degrees Celsius
final temperature = 0.0 degrees Celsius
First, we need to convert the temperatures from degrees Celsius to Kelvin:
initial temperature in Kelvin = -20.0 + 273.15 = 253.15 K
final temperature in Kelvin = 0.0 + 273.15 = 273.15 K
Now, we can calculate the heat required:
heat = 2.0 kg * 2060 J/kg K * (273.15 K - 253.15 K)
heat = 2.0 kg * 2060 J/kg K * 20.0 K
heat = 82,400 J
The heat required to raise the temperature of 2.0 kg of ice from -20.0 degrees Celsius to 0.0 degrees Celsius is 82,400 Joules.