Show that 90 J of work is needed to increase the speed of a 20-kg cart by 3 m/s.
Power =
work done
time interval=
W
t
To solve this problem, we can use the formula for work:
Work (W) = Force × Distance
We know that work (W) is equal to 90 J (joules) and we need to find the power. Power is defined as the work done per unit time and is given by the formula:
Power = Work / Time
So, let's go step by step to find the power (P) using the given information.
Step 1: Find the force (F) applied to the cart.
Since the given information only includes the mass of the cart and the change in speed, we need to find the force acting on the cart. We can use Newton's second law of motion:
Force (F) = Mass (m) × Acceleration (a)
We know the mass of the cart is 20 kg, and the change in speed is 3 m/s. However, we need to convert the change in speed to acceleration. Acceleration is the change in velocity per unit time, so we divide the change in speed (3 m/s) by the time interval it takes for the change to occur. Since we don't have the time interval, let's assume it to be 1 second for simplicity.
Acceleration (a) = Change in speed / Time interval
= 3 m/s / 1 s
= 3 m/s²
Now, we can find the force acting on the cart:
Force (F) = 20 kg × 3 m/s²
= 60 N
Step 2: Calculate the power (P).
Now that we have the force, we can plug it into the power formula:
Power (P) = Work (W) / Time interval
Given that the work done is 90 J, we also need to know the time interval. However, if the time interval is not provided, we cannot directly calculate the power.
So, without the time interval, it is not possible to determine the power required to increase the speed of the 20-kg cart by 3 m/s.