A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 52(angle sign here) downward from the horizontal. Find the work done by the shopper on the cart as the shopper moves along a 50.0 m length of aisle.
Someone tell me if this is right:
W= (35.0N) (50.0m)(cos25.0)
W= 1586 J
If not please show me how to do it.
i had a similar problem, but different #s, and i got it right, so good job, and thanks, cause i didn't know that was how to do it.
To find the work done by the shopper on the cart, you need to multiply the force exerted by the shopper by the displacement of the cart in the direction of the force.
Given:
Force exerted by the shopper, F = 35 N
Angle between the force and horizontal, θ = 52°
Length of the aisle, d = 50.0 m
First, you need to calculate the component of the force in the direction of motion. This can be done using trigonometry.
1. Find the horizontal component of the force:
F_horizontal = F * cos(θ)
F_horizontal = 35 N * cos(52°)
Next, you can calculate the work done by multiplying the horizontal force by the displacement in the same direction.
2. Calculate the work done:
Work = F_horizontal * d
Work = (35 N * cos(52°)) * 50.0 m
Now you can solve this equation to find the work done:
Work = (35 N * cos(52°)) * 50.0 m
Work ≈ 1547.62 J
Therefore, the correct answer is approximately 1547.62 J, not 1586 J.
To find the work done by the shopper on the cart, you need to calculate the component of force in the direction of motion and multiply it by the distance traveled.
Given:
Force applied = 35 N
Angle of force with respect to the horizontal = 52 degrees
Distance traveled = 50.0 m
To calculate the component of force in the direction of motion, use trigonometry. You can decompose the force into its horizontal and vertical components using the given angle.
1. Calculate the horizontal component of force:
Horizontal component = Force × cos(angle)
Horizontal component = 35 N × cos(52 degrees)
2. Calculate the work done:
Work = Force × distance × cos(angle)
Work = Horizontal component × distance
Work = (35 N × cos(52 degrees)) × 50.0 m
To solve this expression, first convert the angle from degrees to radians:
1 degree = π/180 radians
52 degrees = (52 × π)/180 radians
Now, substitute the value of the angle and calculate:
Work = (35 N × cos((52 × π)/180)) × 50.0 m
Using a scientific calculator or software, calculate the cosine value and simplify:
Work ≈ 27.85 N × 50.0 m
Finally, calculate the work:
Work ≈ 1392.5 J
Therefore, the correct value of work done by the shopper on the cart is approximately 1392.5 Joules (J), not 1586 J.