SPH 4Ukinematics & Dynamics Review
SPH 4UKinematics & Dynamics Review
- With what velocity must a soccer ball be kicked in order to hit a 2.6 m high crossbar from a distance of 35 m? Neglect air resistance and assume that the launch angle is 30˚above the horizontal. Also, calculate the maximum height of the ball and its velocity as it just hits the crossbar. 21.3 m/s, 30˚ above H; 20.1 m/s, 23˚ below H
- Steve decides to build a waterslide to launch unsuspecting physics students into the river. The slide is straight, sloped at 30˚and has a 6.0 m vertical drop. The bottom of the slide is 4.0 m above the water. Dan starts at the top with zero velocity, slides down the incline where the coefficient of friction is 0.19 and makes a less than graceful entry into the river.
a)What is his acceleration on the incline?3.27 m/s2
b)With what velocity does he leave the slide?8.86 m/s
c)How far does he go horizontally from the end of the slide to when he hits the water? 4.26 m
d)With what velocity does he enter the water?12.6 m/s, 52˚ below H
- The PM and his premiers are running around in an ever decreasing circle. At the present time it has a radius of 8.0 m. Each counter-clockwise lap take 5.3 s (close to world record?).
a)Calculate the centripetal acceleration at the time when they are running SE.11 m/s2 [NE]
b)Calculate their average acceleration in the time interval from when they are running south to when they are running east. 10 m/s2 [NE]
4.a)Draw a free body diagram to show the forces on a car going around a banked curve at greater than the design speed. Show the horizontal and vertical components of the forces.
b)Write down the equations for the net horizontal and vertical forces.
5.The astronauts in an Apollo spacecraft circled the moon once every 6.5 x 103 seconds. They were about 1.7 x 106 m from the centre of the moon.
a)What was their centripetal acceleration?1.6 m/s2
b)Calculate the mass of the moon.6.9 x 1022 kg
6.Do this question from basic free body diagrams. A curve of radius 280 m is being designed in a new highway to allow cars travelling at 90 km/h to round the curve with zero friction forces.
a)At what angle must the road be banked?12.8˚
b)What is the minimum coefficient of friction that will allow a car to successfully go around the curve at 130 km/h? 0.223
7.For the diagram below calculate the acceleration of the masses and the tension in the light non-stretching string that passes over the light frictionless pulley.
5.12 m/s2; 234 N
8.Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If the maximum force that his arms can tolerate is 1400 N, what is the maximum speed that he can have at the lowest point in his swing? His mass is 82 kg; the vine is 14.0 m long. 10 m/s
SPH 4UMomentum & Energy Review
- For a mass vibrating up and down on the end of a long ideal spring, describe the relationship of kinetic energy, gravitational potential energy and elastic potential energy in the various parts of the cycle (top, bottom & middle).
- A mass of 15.0 kg is dropped from a height of 25 m above the top of a spring. If the spring constant is 1250 N/m, how far will the spring compress before the mass stops falling? (25 cm)
- A 4.0 kg mass, A, moving east at 6.0 m/s has a straight line elastic collision with a 6.0 kg mass, B, moving west at 4.0 m/s. What are the velocities of the two masses of the two masses after the collision? (4 m/s R, 6 m/s L)
- a)What does the force : extension graph look like for a Hooke’s Law spring?
b)What does the area beneath the curve represent?
c)If the spring were to reach its elastic limit, how does the graph change?
d)What would happen to the spring if it was stretched beyond this limit?
e)If the maximum extension using a 0.500 kg mass is 12 cm for this spring, how far would it fall from no-load? (24 cm)
- An 8.0 kg mass moving west at 12.0 m/s has a two-dimensional horizontal collision with a 6.0 kg mass moving directly north at 16.0 m/s. Immediately after the collision, the 8.0 kg mass is moving [N 30°W] at 10.8 m/s.
a)What is the velocity of the 6.0 kg mass after the collision?(9.48 m/s [N 68° W])
b)What is the elasticity of the collision?(0.55)
The following stroboscopic image shows an object (mass 100 g) propelled horizontally by an elastic spring. The object slides first along a smooth surface (ie. frictionless) and then encounters a rough surface (k = 0.12) at the 80 cm mark as indicated on the diagram. The frequency of the strobe is 10 Hz. A centimetre scale has been placed along the object’s path.
By taking measurements and making appropriate calculations, determine
a)the speed of projection when the object first leaves the spring
b)the “k-value” of the spring
c)the loss of energy over the rough surface
d)the speed of the mass at the last position
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