Answer:
A) a = 5.673 m/s²
The direction will be upwards vertically towards the point where it is suspended.
B) T = 113.2 N
Explanation:
A) We are given;
Weight of bowling ball; W = 71.7 N
Speed; v = 4.6 m/s
Rope length; r = 3.73 m
Now, formula for the centripetal acceleration is;
a = v²/r
Thus; a = 4.6²/3.73
a = 5.673 m/s²
The direction will be upwards vertically towards the point where it is suspended.
B) since weight is 71.7 N, it means that;
Mass = weight/acceleration = 71.7/9.8
Mass(m) = 7.316 kg
Thus,
Centripetal force is;
F_cent = 7.316 × 5.673
F_cent = 41.5 N
Thus, Tension in the rope is;
T = W + F_cent
T = 71.7 + 41.5
T = 113.2 N
If there is no air resistance, the value would still be the same. So therefore, the answer is 39.7 N.
Supposing that there is an air resistance of 19.8 N.With a 19.8 N air resistance: ∑F = 39.7 N - 19.8 N = 19.9 N would be the net force. The important point here is that the force of gravity equivalent the weight of the object.
Explanation:
The total resistance Rt is given by
1/Rt = 1/Ra + 1/Rb + 1/Rc = 1/5 + 1/4 + 1/7 = 0.593
or Rt = 1.69 ohms
The total current I running through the circuit is
I = V/Rt = 2.37 A
Answer:
75 rad/s
Explanation:
The angular acceleration is the time rate of change of angular velocity. It is given by the formula:
α(t) = d/dt[ω(t)]
Hence: ω(t) = ∫a(t) dt
Also, angular velocity is the time rate of change of displacement. It is given by:
ω(t) = d/dt[θ(t)]
θ(t) = ∫w(t) dt
θ(t) = ∫∫α(t) dtdt
Given that: α (t) = (6.0 rad/s4)t² = 6t² rad/s⁴. Hence:
θ(t) = ∫∫α(t) dtdt
θ(t) = ∫∫6t² dtdt =∫[∫6t² dt]dt
θ(t) = ∫[2t³]dt = t⁴/2 rad
θ(t) = t⁴/2 rad
At θ(t) = 10 rev = (10 * 2π) rad = 20π rad, we can find t:
20π = t⁴/2
40π = t⁴
t = ⁴√40π
t = 3.348 s
ω(t) = ∫α(t) dt = ∫6t² dt = 2t³
ω(t) = 2t³
ω(3.348) = 2(3.348)³ = 75 rad/s
Answer:
The horizontal velocity is 
Explanation:
From the question we are told that
The mass of the pumpkin is 
The distance of the the car from the building's base is 
The height of the roof is 
The height is mathematically represented as
Where g is the acceleration due to gravity which has a value of 
substituting values
making the time taken the subject of the formula
The speed at which the pumpkin move horizontally can be represented mathematically as
substituting values
