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A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of angle theta as it slides

Solve the heat conduction equation:

for the following boundary and initial conditions:

u(0,t) = u(5,t) = 0,

u(x,0) =2sin(πx)− 4sin(2πx)

for the following boundary and initial conditions:

u(0,t) = u(5,t) = 0,

u(x,0) =2sin(πx)− 4sin(2πx)

Question 20

A block of mass 1.8kg is at rest on a smooth horizontal table. The block is connected to a hanging mass of 2kg, by a light inextensible string and frictionless pulley system as shown in Figure 5. The hanging mass is then released from rest. Determine;

(a) The acceleration of the block/hanging mass system (b) The tension in the string.

A block of mass 1.8kg is at rest on a smooth horizontal table. The block is connected to a hanging mass of 2kg, by a light inextensible string and frictionless pulley system as shown in Figure 5. The hanging mass is then released from rest. Determine;

(a) The acceleration of the block/hanging mass system (b) The tension in the string.

Question 19

A coin placed 0.4m from the centre of a rotating, horizontal turntable slips when its speed is 0.6 m/s. What is the coefficient of static friction between the coin and turntable?

A coin placed 0.4m from the centre of a rotating, horizontal turntable slips when its speed is 0.6 m/s. What is the coefficient of static friction between the coin and turntable?

The position of a particle which is constrained to move along a straight line is given by

x = 3t3 − 7t + 9 , where x is the position measured in metres from an origin and t is in seconds. Determine the acceleration of the particle when its velocity is 26 m/s.

x = 3t3 − 7t + 9 , where x is the position measured in metres from an origin and t is in seconds. Determine the acceleration of the particle when its velocity is 26 m/s.

The Niagara River delivers an average of 5470 m3 of water per second to the top of Niagara Falls, where it drops 48.5 m. If all the potential energy of that water could be converted to electrical energy, how much electrical power could Niagara Falls generate? (Note: The mass of 1 m3 of water is 1000 kg).

A mass of 3 kg is to rest vertically over a spring with a spring constant, k, of 1400 N/m. What is the energy absorbed by the spring?

A rocket of mass 14500kg accelerates at 210m/s2 for 32s from an initial speed of 5100m/s. (a) How fast will be rocket be travelling after the 32s?

(b) How much Kinetic Energy has the rocket gained?

(b) How much Kinetic Energy has the rocket gained?

Question 14

A radar station at O tracks two ships P & Q. P has position vector (2i + 4j) km, and Q has position vector (7i + 6j) km. What is the magnitude of the distance between ships?

A radar station at O tracks two ships P & Q. P has position vector (2i + 4j) km, and Q has position vector (7i + 6j) km. What is the magnitude of the distance between ships?

A ball is left to drop, from rest, vertically from the top of a building from a position 48 m above ground.

i. What is the distance travelled by the ball after it has been falling for 3 seconds?

ii. What is the downwards velocity of the ball as it strikes the ground?

i. What is the distance travelled by the ball after it has been falling for 3 seconds?

ii. What is the downwards velocity of the ball as it strikes the ground?