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zepelin [54]
3 years ago
10

A shopper pushes a grocery cart 41.9 m on level ground, against a 44.5 N frictional force. The cart has a mass of 16.3 kg. He pu

shes in a direction 17.5º below the horizontal. If the initial velocity was 1.9 m/s, and final speed was 12.6 m/s. What is the work done by the pushing force in unit of Joule?
Physics
1 answer:
Rashid [163]3 years ago
5 0

Answer:

Fp = 26.59[N]

Explanation:

This problem can be solved using the principle of work and energy conservation, i.e. the final kinetic energy of a body will be equal to the sum of the forces that do work on the body plus the initial kinetic energy.

We need to identify the initial data:

d = distance = 41.9[m]

Ff = friction force = 44.5 [N]

m = mass = 16.3 [kg]

v1 = 1.9 [m/s]

v2 = 12.6 [m/s]

The kinetic energy at the beginning can be calculated as follows:

E_{k1}= \frac{1}{2}*m*v_{1}^2 \\E_{k1}= \frac{1}{2}*16.3*(1.9)_{1}^2\\E_{k1}= 29.42[J]

And the final kinetic energy.

E_{k2}= \frac{1}{2}*m*v_{2}^2 \\E_{k2}= \frac{1}{2}*16.3*(12.6)^2\\E_{k2}= 1294[J]

The work is performed by two forces, the friction force and the pushing force, it is important to clarify that these forces are opposite in direction.

The weight of the cart also performs a work in the direction of movement since the plane is tilted down, this component of the weight of the cart must be parallel to the surface of the inclined plane.

W_{1-2}=-(44.5*41.9)+(16.3*9.81*sin(17.5)*41.9)+(F_{p}*41.9) \\therefore:\\E_{k1}+W_{1-2}=E_{k2}\\29.42+150.16+(F_{p}*41.9)=1294\\F_{p}=1114.42/41.9\\F_{p}=26.59[N]

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Answer:

a) The total time of the trip is 4.05 h.

b) The average speed of the car is 12.35 mi/h.

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Explanation:

Hi there!

a) The equation of traveled distance for a car traveling at constant speed is the following:

x= v · t

Where:

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t = time.

Solving the equation for t, we can find the time it takes to travel a given distance "x" at a velocity "v":

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t2= 25.0 mi / 52.00 mi / h

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b) The average speed (a.s) is calculated as the traveled distance (d) divided by the time it takes to travel that distance (t). In this case, the traveled distance is 50 mi and the time is 4.05 h. Then:

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