A two man bobsled is pushed along a horizontal, frictionless track by the brakeman. The driver and
bobsled have a mass of 280 kg. The brakeman pushes with a net force of 160 N a distance of 50
m. What is the final speed of the bobsled just before the brakeman jumps into the sled? The sled
was pushed for 6.61 s. How much power does the brakeman expend on the sled?
v^2 = 2as = 2(160/280)(50) = 57.14
so v = 7.56 m/s
power = force*distance/time
so plug in your numbers
To find the final speed of the bobsled, we can use the work-energy principle.
1. Calculate the work done by the brakeman:
Work = Force * Distance
Work = 160 N * 50 m
Work = 8000 J
2. Use the work-energy principle to find the change in kinetic energy:
Change in Kinetic Energy = Work
Change in Kinetic Energy = 8000 J
3. Calculate the initial kinetic energy:
Initial Kinetic Energy = 1/2 * mass * (initial velocity)^2
Since the bobsled starts from rest, the initial velocity is 0, so the initial kinetic energy is 0 J.
4. Use the change in kinetic energy to find the final kinetic energy:
Final Kinetic Energy = Initial Kinetic Energy + Change in Kinetic Energy
Final Kinetic Energy = 0 J + 8000 J
Final Kinetic Energy = 8000 J
5. Use the final kinetic energy to find the final speed:
Final Kinetic Energy = 1/2 * mass * (final velocity)^2
8000 J = 1/2 * 280 kg * (final velocity)^2
6. Solve for the final velocity:
(final velocity)^2 = (8000 J) / (1/2 * 280 kg)
(final velocity)^2 = 57.14 m^2/s^2
final velocity = √57.14
final velocity ≈ 7.56 m/s
Therefore, the final speed of the bobsled just before the brakeman jumps into the sled is approximately 7.56 m/s.
To calculate the power expended by the brakeman, we can use the formula:
Power = Work / Time
7. Calculate the power:
Power = 8000 J / 6.61 s
Power ≈ 1210.29 Watts
Therefore, the brakeman expends approximately 1210.29 Watts of power on the sled.
To find the final speed of the bobsled, we can use the principle of work and energy.
1. First, let's calculate the work done by the brakeman using the equation:
Work = Force x Distance
Given:
Force = 160 N
Distance = 50 m
Work = 160 N x 50 m = 8000 J (Joules)
2. Next, we can find the change in kinetic energy using the equation:
Work = Change in Kinetic Energy
The initial kinetic energy is 0 since the bobsled starts from rest. So the change in kinetic energy is equal to the work done by the brakeman.
Change in Kinetic Energy = 8000 J
3. We can now find the final speed (v) of the bobsled. The equation to calculate kinetic energy is:
Kinetic Energy = (1/2) x Mass x (Velocity)^2
Rearranging the equation to solve for velocity:
Velocity = sqrt((2 x Kinetic Energy) / Mass)
Given:
Mass = 280 kg
Change in Kinetic Energy = 8000 J
Velocity = sqrt((2 x 8000 J) / 280 kg) = 16.91 m/s (rounded to two decimal places)
Therefore, the final speed of the bobsled just before the brakeman jumps into the sled is approximately 16.91 m/s.
Now let's calculate the power expended by the brakeman.
Power is defined as the rate at which work is done. It can be calculated using the equation:
Power = Work / Time
Given:
Work = 8000 J
Time = 6.61 s
Power = 8000 J / 6.61 s = 1210.44 W (Watts)
Therefore, the brakeman expends approximately 1210.44 Watts of power on the sled.