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Pie
3 years ago
5

A 2.4 kg box has an initial velocity of 3.6 m/s upward along a plane inclined at 27◦ to the horizontal. The coefficient of kinet

ic friction between the box and the plane is 0.12. The acceleration of gravity is 9.81 m/s 2 . How far up the incline does the box travel? Answer in units of m.
Physics
1 answer:
Vika [28.1K]3 years ago
7 0

Answer:

d= 1.18 m

Explanation:

In abscense of  friction, total mechanical energy must be constant, i.e.,

ΔK + ΔU = 0

As we are told that there exists a kinetic friction between the box and the plane, we need to take into account the work done by the friction force in the equation, as follows:

ΔK + ΔU = Wnc (1)

If we take as our zero gravitational potential energy reference, the height at which the box is sent upward, we can write the following equations for the different terms in (1):

ΔK = Kf- K₀ = 0 - 1/2*m*v₀² = -1/2*2.4kg* (3.6)²(m/s)² = -15.6 J

ΔU = Uf - U₀ = m*g*h = *m*g*d*sin θ = 2.4 kg*9.81 m/s²*d*0.454 = 10.7*d J

Wnc = Ff. d* cos (180º) = μk*N*d*cos(180º) (2)

The friction force always opposes to the displacement, so the angle between force and displacement is 180º.

The normal force, as is always perpendicular to the surface, takes the value needed to equilibrate the component of the weight perpendicular to the incline, as follows:

N = m*g*cosθ =  2.4 kg*9.81 m/s²*cos 27º = 21 N

Replacing in (2):

Wnc = 0.12*21*cos (180º) = -2.52*d J

Replacing in (1):

-15.6 J + 10.7*d J = -2.52*d J

Solving for d:

d = 1.18 m

 

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2 years ago
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3 years ago
Finish A 16 N force is applied to an object and 96 J of work is done. How far was the object moved?
Lina20 [59]

Answer:

\boxed {\boxed {\sf 6 \ meters}}

Explanation:

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We know that 96 Joules of work were done and a 16 Newton force was applied to the object.

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Substitute the values into the formula.

96 \  J= 16 \ N * d

First, let's convert the units. This will make cancelling units easier later in the problem. 1 Joule (J) is equal to 1 Newton meter (N*m), so the work of 96 Joules equals 96 Newton meters.

96 \ N*m= 16 \ N * d

Now, solve for distance by isolating the variable, d. It is being multiplied by 16 Newtons and the inverse of multiplication is division. Divide both sides of the equation by 16 N.

\frac {96 \ N*m}{16 \ N}= \frac{16 \ N *d}{16 \ N}

\frac {96 \ N*m}{16 \ N}=d

The units of Newtons cancel.

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3 years ago
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viktelen [127]

Answer:

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We need to find the distance covered by car if the force continues to be applied to the car. Firstly, lets find the acceleration of the car:

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Let d is the distance covered by car. Using second equation of motion as :

d=ut+\dfrac{1}{2}at^2\\\\d=11.17\times 35+\dfrac{1}{2}\times 0.632\times (35)^2\\\\d=778.05\ m

So, the car will cover a distance of 778.05 meters.

5 0
3 years ago
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