Hi there!
Recall Newton's Second Law:

∑F = Net force (N)
m = mass (kg)
a = acceleration (m/s²)
We are already given the mass and acceleration, so we can plug these values into the equation:
∑F = 1600 · 4.5 = 7200 N
Answer:
a) 1. 1365 × 10⁻⁹N
b) 9.1862 × 10⁻⁴⁶N
c) 8.61 × 10⁻¹¹C/Kg
Explanation:
Ke = 8.99× 109 N.m2
/ C2
, G = 6.67 × 10-11 N. m2
/ kg2
a) F = Ke . q₁.q₂/r²
= (8.99× 109 N.m2
/ C2
) ×(1.60×10⁻¹⁹C)²/(4.50×10⁻¹⁰C)²
= 1. 1365 × 10⁻⁹N
b)
F = Gm₁m₂/r²
= (6.67× 10⁻¹¹)×(1.67×10⁻²⁷)²/(4.50×10⁻¹⁰)²
= 9.1862 × 10⁻⁴⁶N
The electric force is larger by 8.0497 ×10³⁷ times
c)
if Keq₁q₂/r² Gm₁m₂/r²,
with q₁=q₂ = q, and m₁ =m₂ = m
Then q/m =
= 
= 8.61 × 10⁻¹¹C/Kg
constant non zero acceleration
Answer:
The percentage change in frequency is 10%.
Explanation:
Given that,
Amplitude decreases by 1/10 per second.
Resonance = 10 Hz
We need to calculate the change in frequency
Using formula of change in frequency

Put the value into the formula


We need to calculate the resonant frequency
Using formula of resonant frequency

Put the value into the formula


We need to calculate the percentage change in frequency
Using formula of percentage change in frequency


Hence, The percentage change in frequency is 10%.
Answer:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°
Explanation:
From the question given above, the following data were obtained:
Range (R) = 65 m
Time of flight (T) = 3 s
Acceleration due to gravity (g) = 10 m/s²
Lauch velocity (u) =?
Lauch Angle (θ) =?
R = u²Sin2θ /g
65 = u² × Sin2θ /10
Recall:
Sin2θ = 2SinθCosθ
65 = u² × 2SinθCosθ / 10
65 = u² × SinθCosθ / 5
Cross multiply
65 × 5 = u² × SinθCosθ
325 = u² × SinθCosθ .....(1)
T = 2uSinθ / g
3 = 2uSinθ / 10
3 = uSinθ / 5
Cross multiply
3 × 5 = uSinθ
15 = u × Sinθ
Divide both side by Sinθ
u = 15 / Sinθ....... (2)
Substitute the value of u in equation (2) into equation (1)
325 = u² × SinθCosθ
u = 15 / Sinθ
325 = (15 / Sinθ)² × SinθCosθ
325 = 225 / Sin²θ × SinθCosθ
325 = 225 × SinθCosθ / Sin²θ
325 = 225 × Cosθ / Sinθ
Cross multiply
325 × Sineθ = 225 × Cosθ
Divide both side by Cosθ
325 × Sineθ / Cosθ = 225
Divide both side by 325
Sineθ / Cosθ = 225 / 325
Sineθ / Cosθ = 0.6923
Recall:
Sineθ / Cosθ = Tanθ
Tanθ = 0.6923
Take the inverse of Tan
θ = Tan¯¹ 0.6923
θ = 35°
Substitute the value of θ into equation (2) to obtain the value of u.
u = 15 / Sinθ
θ = 35°
u = 15 / Sin 35
u = 15 / 0.5736
u = 26.15 m/s
Summary:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°