You are travelling in your 2000 kg car at 12.5 m/s and wish to accelerate to 17.3 m/s in 4.28 seconds, how much work, to the nearest joule, is required?
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4
In the previous problem what is the average power to the nearest watt?
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5
Assuming you have a bow that behaves like a spring with a spring constant of 150 N/m and you pull it to a draw of 51 cm, to the nearest joule how much work do you perform?
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6
In the previous problem, to the nearest tenth of a m/s, what is the speed of the 52 gram arrow when it is released?
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7
The green block is falling at a speed of 21 m/s and is 9 meters above the spring. The spring constant is 3840 N/m, to the nearest tenth of a cm how far is the spring compressed?
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8
In the previous problem to the nearest hundredth of a meter to what height will the block rise after it hits and leaves the spring?
To calculate the amount of work required in each of these problems, you need to use the formula for work:
Work (W) = Force (F) * Distance (d) * cos(theta)
In problem 4, you are given the mass of the car (2000 kg), initial velocity (12.5 m/s), final velocity (17.3 m/s), and the time taken (4.28 s). To find the work, you need to find the change in kinetic energy of the car.
1. Calculate the initial kinetic energy (KE_initial) using the formula:
KE_initial = (1/2) * mass * (initial velocity)^2
2. Calculate the final kinetic energy (KE_final) using the formula:
KE_final = (1/2) * mass * (final velocity)^2
3. Calculate the change in kinetic energy (ΔKE) by subtracting KE_initial from KE_final:
ΔKE = KE_final - KE_initial
4. The work done is equal to the change in kinetic energy:
Work = ΔKE
To find the average power in problem 5, you need to divide the work done (which can be calculated using the same steps as problem 5) by the time taken (assuming a time of 4 seconds).
Average Power = Work / Time
In problem 6, you are given the spring constant (150 N/m) and the draw distance (51 cm). To find the work, you need to calculate the potential energy stored in the spring.
1. Convert the draw distance from centimeters to meters (51 cm = 0.51 m).
2. Calculate the potential energy (PE) stored in the spring using the formula:
PE = (1/2) * spring constant * (draw distance)^2
3. The work done is equal to the potential energy stored in the spring:
Work = PE
To find the speed of the arrow in problem 7, you can use conservation of energy.
1. Calculate the gravitational potential energy (PE_gravity) using the formula:
PE_gravity = mass * gravity * height
2. Calculate the potential energy stored in the spring (PE_spring) using the formula (as calculated in problem 6).
3. The total initial energy is the sum of PE_gravity and PE_spring.
4. The total final energy is the kinetic energy (KE) of the arrow.
5. Set the initial energy equal to the final energy and solve for the final velocity using the formula:
KE = (1/2) * mass * (final velocity)^2
In problem 8, you can use the same approach as problem 7 to find the compression of the spring. However, instead of calculating the final velocity, you need to calculate the height that the block will rise after leaving the spring. To find this height, you can use the conservation of mechanical energy.
1. Calculate the gravitational potential energy (PE_gravity) using the formula used in problem 7.
2. Calculate the potential energy stored in the spring (PE_spring) using the spring constant and the compression of the spring (as calculated in problem 7).
3. The total initial energy is the sum of PE_gravity and PE_spring.
4. The total final energy is the potential energy of the block at its highest point (when its velocity becomes zero).
5. Set the initial energy equal to the final energy and solve for the height.