How much force must be applied to make a 4.75 kg block just start to move up an incline set at 60 , the coefficient of friction is \( \square \mathrm{s}=0.23 \) ? \[ 2<2 / 2 \]
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To calculate the force required to start moving the block up the incline, we first need to consider both the gravitational force acting down the slope and the frictional force opposing the motion. The force due to gravity can be calculated as \( mg \sin(\theta) \), where \( m \) is the mass, \( g \) is the acceleration due to gravity (~9.81 m/s²), and \( \theta \) is the angle of the incline (60°). The normal force is \( N = mg \cos(\theta) \), and the force of friction is given by \( f_f = \mu N \), where \( \mu \) is the coefficient of friction (0.23). We can thus sum up these forces to find the total force required to get the block moving: 1. Calculate gravitational force down the incline: \( F_g = 4.75 \, \text{kg} \times 9.81 \, \text{m/s}² \times \sin(60°) \). 2. Calculate normal force: \( N = 4.75 \, \text{kg} \times 9.81 \, \text{m/s}² \times \cos(60°) \). 3. Calculate frictional force: \( f_f = 0.23 \times N \). 4. Total force required to overcome both gravity and friction: \( F = F_g + f_f \). Plug in the numbers, and you should find that you need to apply a force of approximately 38.63 N to get the block just starting to move up the incline!
