Elasticity

1. Find the maximum load which may be placed on a steel wire of diameter 1.0 mm if the permitted strain must not exceed 1/1000 and the Young modulus for steel is 2.0 x 10¹¹ Pa. [Answer: 157 N]

2. A uniform steel wire of length 4 m and cross-sectional area of 3 x 10^-6 m² is extended 1 mm. Calculate the energy stored in the wire if the elastic limit is not exceeded. (Young modulus = 2.0 x 10¹¹ Pa) [Answer: 0.075 J]

3. Two vertical wires X and Y, suspended at the same horizontal level, are connected by a light rod XY at their lower ends. Two wires have the same length l and cross-sectional area A. A weight of 30 N is placed at O on the rod, where XO:OY = 1:2. Both wires are stretched and the rod XY then remains horizontal. If the wire X has Young modulus E₁ of 1.0 x 10¹¹ Nm^-2, calculate the Young modulus E₂ of the wire Y assuming the elastic limit is not exceeded for both wires. [Answer: 5.0 x 10¹⁰ Pa]

4. A rubber cord of a catapult has a cross-sectional area of 2 mm² and the initial length of 0.20 m, and is stretched to 0.24 m to fire a small object of mass 10 g. Calculate the initial velocity of the object when it just leaves the catapult. Assume the Young modulus for rubber is 6 x 10⁸ Pa and that the elastic limit is not exceeded. [Answer: 31 m/s]

5. A ball is dropped from the top of a building of 150 m. One second later, another ball is thrown up vertically from ground with velocity of 55.0 m/s. When and where will the two balls meet? [Answer: 2.2308 s, 97.81 m]

6. A skater with an initial speed of 7.60 m/s is gliding across the ice. Air resistance is negligible. The coefficient of kinetic friction between the ice and the skate blades is 0.100. Find the deceleration cause by kinetic friction. How far will the skater travel before coming to rest? [Answer: 1.0 m/s², 28.88 m]

7. A shopper in a supermarket pushes a loaded cart with a horizontal force of 10 N. The cart has a mass of 30 kg. (a) How far will it move in 3.0 s, starting from rest? (b) How far will it move in 3.0 s if the shopper places her 30 N child in the cart before she begins to push it? [Answer: (a) 1.5 m (b) 1.3636 m]

8. A small ball Q, suspended from a string is set into oscillation. When the ball passes through the lowest point of the motion, the string is cut. If the ball is then moving with the velocity of 0.8 m/s at a height of 5 m above the ground, find the horizontal distance traveled by the ball. (Assume g = 10 m/s²) [Answer: 0.8 m]

9. A car moving with a velocity of 10 m/s accelerates uniformly at 1 m/s until it reaches a velocity of 15 m/s. Calculate (i) the time taken, (ii) the distance traveled during the acceleration, (iii) the velocity reached 100m from the place where the acceleration began. [Answer: (i) 15 s (ii) 62.5 m (iii) 17 m/s]

10. A ball is thrown vertically upward with an initial velocity of 20 m/s. Calculate (i) the time taken to return to the thrower, (ii) the maximum height reached. [Answer: (i) 4 s (ii) 20 m]

11. A ball is dropped from a height of 20 m and rebounds with a velocity which is 3/4 of the velocity with which it hit the ground. What is the time interval between the first and second bounces?    [Answer: 3 s]

12. A small smooth object slides from rest down a smooth inclined plane inclined at 30 degree to the horizontal. What is (i) the acceleration down the plane (ii) the time to reach the bottom if the plane is 5 m long? The object is now thrown up the plane with an initial velocity of 15 m/s. (iii) How long does the object take to come to rest? (iv) How far up the plane has the object then traveled?  [Answer: (i) 5 m/s² (ii) 1.4 s (iii) 3 s (iv) 22.5 m]

13. A ball is thrown forward horizontally from the top of a cliff with a velocity of 10 m/s. the height of the cliff above the ground is 45 m. Calculate (i) the time to reach the ground, (ii) the distance from the cliff of the ball on hitting the ground, (iii) the direction of the ball to the horizontal just before it hits the ground. [Answer: (i) 3 s (ii) 30 m (iii) 72 degree]

14. Projectiles containing delicate electronics equipment may be damaged if they are subjected to high acceleration. For this reason, such projectiles may be fired from guns with long barrels but not from guns with short barrels. (a) State two factors which affect the range of a projectile fired from a gun. (b) Explain why a projectile fired from a long-barreled gun is subjected to less acceleration than a short-barreled gun if the range is the same in both cases. (c) Draw a free-body force diagram for a projectile just after it has left the barrel of a gun. [Answer: Not provided]