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. : "Mechanics"

Mechanics: Translation and Rotation

Q- A block of mass m = 10 kg is pulled from rest, on a horizontal surface by a massless rope passing over a pulley of same mass m = 10 kg, radius R = 0.25 m and moment of inertia I = 1.2 kg m2, rotates freely about its axis. The force applied at the end of the rope is P = 750 N. If the coefficient…

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Vectors: Force

Q- To pull a car, one end of a rope 25 m long is attached to the car. The other end is fastened to a tree. A man exerts a force of 500 N at the midpoint of the rope pulling it 1 meter to the side. What is the force exerted on the car in this position?

Solution:

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Center Of Mass

Q- Three particles, each with a mass of 0.25 kg, are located at ( - 4.0 m, 0), (2.0 m, 0), and (0, 3.0 m) and are acted on by forces F1 = 3 N along negative y-direction, F2 = 5 N along positive y-direction and F3 = 4 N along x direction  respectively. Find  position of center of mass of the system a…

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Head-on Collision

Q- A 1000 kg car traveling east at 25 mph gets rear-ended hit by a truck weighing 1500 kg also moving east. After collision the vehicles lock bumpers and continue moving east at 40 mph.

(a) What was the original speed of the truck

(b) How much kinetic energy of the system lost during this collisi…

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Circular Motion

Q- A 63 g ball is whirled in a horizontal circle of radius 60 cm, on the end of a cord that makes an angle of 180 with the horizontal. Find

(a) The tension in the string. And

(b) The speed of the ball.

Solution:

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Mechanics: Conservation Of Energy

(On request - Manish)

Q- Two blocks are connected by a light cord passing over a frictionless pulley. Their masses are m1 = 3 kg and m2 = 2 kg and the ramp is frictionless. At position A the block m1 is sliding up at velocity 2.5 m/s. Find the speed of the block at position B.

Solution:

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Vectors: Force

Q- The leg and cast in the figure weigh W = 210 N, with the center of mass as indicated by blue arrow. The counter balance W1 = 140 N. Determine the weight W2 and the angle α needed so that no force exerted on the hip joint by the leg and cast.

Solution:

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Circular Motion

Q- A disk accelerates constantly from rest. After 8 s, it has made 3 revolutions.

(a)  What is the angular acceleration of the disk?

(b) What is the angular velocity of the disk at t = 8 s?

(c) If the radius of the disk is 50 cm, what is the linear velocity of a point on the rim at time t = 8 s?

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Mechanics: Conservation of Energy

Q- A roller coaster car of mass 1000 kg is riding along a track from point A to point C as in figure. (g = 10 m/s2)

(a) Assuming no friction between the track and the car, what is the speed of the car at the top of first hill A?

(b) What is the speed of the car at the top of second hill B?

(c) Wh…

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Vectors: Parallel Forces

Q- The horizontal bar is acted upon by four vertical forces as shown in the figure. What is the horizontal distance from point O to the line of action of the resultant of the given forces?

Solution:

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Momentum

Q- A 5 kg fish swimming at 2 m/sec swallows an absent minded 1 kg fish swimming toward it at a velocity that brings both fish to a halt immediately after lunch. What is the velocity of the smaller fish before lunch?

Solution:

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Collision

Q- A truck with mass 5000 kg is heading east at 20 m/s. Meanwhile a car with mass 2500 kg is heading north at 30 m/s. The two vehicles collide at an intersection, get stuck together and the wreckage keeps moving to some direction.

(a) Is the collision elastic or inelastic?

(b) Find the speed of th…

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Vectors: Resolution

Q- Figure shows four concurrent forces in equilibrium. Find the magnitude and direction of F3 and F4.

Solution:

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