ok it says
a shopper in a supermarket pushes a cart with a force of 36N directed at an angle of 26 degrees downward from the horizontal.
find the work done by the shopper on the cart as the shopper moves along a 50.6m length of aisle. answer in units of J.
ok so i did.
w=Fd(cos0)
[36N(cos26)]*50.6m
=1178.428
im i doing it right?
Yes, you are on the right track!
To find the work done by the shopper on the cart, you need to calculate the dot product of the force and the displacement. The formula for calculating work is:
Work = Force * Displacement * cos(theta)
In this case, the force is given as 36N, the displacement is 50.6m, and the angle theta is 26 degrees. So you can use the formula you mentioned:
Work = 36N * 50.6m * cos(26 degrees)
Make sure to convert the angle to radians before taking the cosine. Then, plug in the values in the equation:
Work = 36N * 50.6m * cos(26 degrees)
= 36 N * 50.6 m * cos(0.4539 radians)
≈ 1178.43 J
Therefore, the work done by the shopper on the cart as they move along the aisle is approximately 1178.43 J.
Yes, you are on the right track, but there is a small mistake in your calculation. Let's go through the steps to find the correct answer.
To find the work done by the shopper on the cart, we can use the formula:
Work = Force * Distance * cos(θ)
Where:
- Work is the work done by the force (measured in Joules, J)
- Force is the magnitude of the applied force (measured in Newtons, N)
- Distance is the length of the aisle (measured in meters, m)
- θ is the angle between the applied force and the direction of motion (in degrees)
In this case, you correctly identified the force as 36 N and the distance as 50.6 m. However, the angle you provided (26 degrees) is the angle downward from the horizontal, not the angle between the applied force and the direction of motion.
Since the force is directed downward at an angle of 26 degrees, the angle between the applied force and the direction of motion is the complement of that angle, which is 90 degrees minus 26 degrees.
So, the correct angle to use is: θ = 90° - 26° = 64°.
Plugging these values into the formula, we have:
Work = 36 N * 50.6 m * cos(64°)
Using a scientific calculator or trigonometric table, evaluate cosine of 64 degrees to get the decimal value (approximately 0.438).
Work = 36 N * 50.6 m * 0.438 ≈ 796.73088 J
Therefore, the correct answer, rounded to three significant figures, is approximately 796.731 J.
So, your answer of 1178.428 J is incorrect.