1. Three particles each with a mass of 1 kg are at the vertices of an equilateral triangle whose sides are 1 m long. How large is the gravitational force experienced by each point particle (in G)?
Solution
The magnitude of the gravitational force experienced by one of the particles.
F12 = G (m1)(m2) / r2 = G (1)(1) / 12 = G/1 = G
F13 = G (m1)(m3) / r2 = G (1)(1) / 12 = G/1 = G
Resultant gravitational force at point 1:
1. A conducting ball with a radius of 10 cm has an electric charge of 500 μC. Points A, B, and C lie in line with the center of the ball at a distance of 12 cm, 10 cm and 8 cm respectively from the center of the ball. Calculate the electric field strength at points A, B, and C!
Known:
The radius of the conducting ball (R) = 10 cm = 0.1 m
Electric charge (q) = 500 μC = 500 x 10-6 C
rA = 12 cm = 0,12 m
rB = 10 cm = 0,1 m
rC = 8 cm = 0,08 m
Coulomb constant (k) = 9 x 109
Wanted: The electric field strength at point A (EA), at point B (EB) and at point C (EC)
Solution:
1. A spring in free suspension has a length of 10 cm. At the free end, a 200 gram weight is suspended so that the length of the spring is 11 cm. If g = 10 m/s2, what is the spring force constant?
Known:
The initial length of the spring (y1) = 10 cm = 0.10 m
The final length of the spring (y2) = 11 cm = 0.11 m
Spring length change (Δy) = 0.11 – 0.10 = 0.01 meter
The mass of the load (m) = 200 grams = 0.2 kg
Load weight (w) = m g = (0,2)(10) = 2 Newtons
Wanted: Spring constant (k)
Solution:
1. An electric charge is moved in a homogeneous electric field with a force of 2√3 N a distance of 20 cm. If the direction of the force is at an angle of 30o to the displacement of the electric charge, what is the difference in the electric potential energy at the initial and final positions of the electric charge.
Known:
Force (F) = 2√3 N
Distance (s) = 20 cm = 0.2 m
Angle (θ) = 30o
Wanted: Electric potential difference
Solution:
1. An object moving in a circular path has a radius of 0.5 m. The particle is able to cover an angle of 60π rad in 15 seconds. Determine the angular speed of the object.
Known:
Radius (r) = 0.5 meters
Angle (θ) = 60π rad
Time interval (t) = 15 seconds
Wanted: Angular velocity (ω)
Solution:
1. A car with a mass of 5 tonnes moves from rest in 50 seconds, reaching a speed of 72 km/hour. The force on the car is…
Known:
Mass (m) = 5 tons = 5000 kg
Initial speed (vo) = 0
Final speed (vt) = 72 km/h = 20 m/s
Time interval (t) = 50 seconds
Wanted: Force (F)
Solution:
1. A car with a mass of 250 kg is moving with a speed of 72 km/hour, then accelerated with a constant force so that in 5 seconds its speed becomes 80 km/hour. Determine the impulse for 5 seconds
Known:
The mass of the car (m) = 250 kg
Initial speed (vo) = 72 km/h = 20 m/s
Final speed (vt) = 80 km/h = 22 m/s
Time interval (t) = 5 seconds
Wanted: Determine impulse (I)
Solution:
1. Block A 3 kg is placed on the table and then tied to a rope that is connected to stone B = 2 kg through a pulley as shown. The mass and friction of the pulleys are neglected. Acceleration due to gravity g = 10 m/s2. Determine the acceleration of the system and the tension in the rope if:
a) smooth table
b) rough table with a coefficient of kinetic friction of 0.4
Known:
The mass of block A (mA) = 3 kg
The mass of rock B (mB) = 2 kg
Acceleration due to gravity (g) = 10 m/s2
Weight of block A (wA) = m g = (3)(10) = 30 Newton
Weight of rock B (wB) = m g = (2)(10) = 20 Newton
Wanted: The acceleration of the system (a) and the tension in the rope (T)
Solution:
1. A block has a mass of 5 kg. If g = 10 m/s2, determine:
a) the weight of the block
b) the normal force if the block is placed on a flat plane
c) the normal force if the block rests on an inclined plane that forms an angle of 30o to the horizontal
Known:
The mass of the block (m) = 5 kg
Acceleration due to gravity (g) = 10 m/s2
Wanted: w, N on the plane and N on the incline
Solution:
1. The picture below shows three blocks, namely A, B and C which are located on a smooth horizontal plane. If mass A = 1 kg, mass B = 2 kg and mass C = 2 kg and F = 10 N, then determine the ratio of the tension in the rope between A and B to the tension in the rope between B and C.
Known:
The mass of A (mA) = 1 kg
Mass B (mB) = 2 kg
The mass of C (mC) = 2 kg
Tensile force (F) = 10 N
Wanted: TAB : TBC
Solution:
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