A crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial spped shown in the figure below. The crate is pulled a distance of 8.24m on the incline by a force of 150N force. b) What is the speed of the crate after it is pulled the 8.24M? Answer in units of m/s.

(a) Kinetic energy of the cart is 648.32 J.

(b) Speed of the cart is 11.44 m/s.

Explanation:

From the attached below figure we came to know that,

Mass of the crate is 10 kg (m)

Initial speed of the crate is 1.2 m/s (v)

Coefficient of friction on a rough plane is 0.286 (µ)

Force on the cart is 150 N (F)

The distance which crate is moved (d) is 8.05 m.

Calculation of kinetic energy:

Acceleration of the cart:

We know that,

F = F – m × g × sinθ - µ × m × g × cosθ (F = ma)

m × a =  F – m × g × sinθ - µ × m × g × cosθ

10 × a = 150 – (10 × 9.8 × sin 27) – (0.286 × 10 × 9.8 × cos 27)

10 × a = 150 – 44.49 – 24.97

10 × a = 80.54

Calculation of speed:

Change in kinetic energy = m × a × d

Change in kinetic energy = 10 × 8.054 × 8.05

Change in kinetic energy = 648.32 J

Explanation:

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2